Find the Interest Rate
Discussion
Perhaps I'm being stupid...
Looking at a lease purchase and I've been given a rate of £60/£1000
Straight purchase cost is £7,267.
(£7,267 / 1,000) x 60 giving me £436.02 as a quarterly payment which stacks up with what I've been told.
Over 5 years, so 20 payments... £8,720.40 total repayable. So 1,453.40 is the total interest repayable across the term.
How do I turn this into an interest rate? Where does the £60/£1000 rate come from, it somehow knows it's being paid over 5 years.
Explain it to a simpleton, I'm not a financial brain and usually turn to websites and calculators for this sort of thing, which I have, but not without confusing me as I want an actual explanation rather than just the figures in this instance.
I could be having an off day and missing something obvious.
Looking at a lease purchase and I've been given a rate of £60/£1000
Straight purchase cost is £7,267.
(£7,267 / 1,000) x 60 giving me £436.02 as a quarterly payment which stacks up with what I've been told.
Over 5 years, so 20 payments... £8,720.40 total repayable. So 1,453.40 is the total interest repayable across the term.
How do I turn this into an interest rate? Where does the £60/£1000 rate come from, it somehow knows it's being paid over 5 years.
Explain it to a simpleton, I'm not a financial brain and usually turn to websites and calculators for this sort of thing, which I have, but not without confusing me as I want an actual explanation rather than just the figures in this instance.
I could be having an off day and missing something obvious.
How good a mathematician are you?
It is possible to calculate the APR using long-hand maths, but all those in the industry use calculators for the task.
If you have a financial calculator or even access to Excel, you can do the sums a lot easier.
Rate per thousand is used to enable a quote where the purchase price is not yet known or may vary. But it assumes a few constants. In your case:
Constant repayments are over 20 quarters, payable in arrears. No residual.
The APR of 7.4% is correct (using these assumptions).
The formula for calculating the interest rate is:
PV = R((1+r)n - 1)/r(1+r)n
Where you see "n" above, please read as 'power n' (as I can't denote a power symbol in this text) i.e. (1+r)to the power of n.
This formula will still only give you a quarterly compound interest rate, which would then need to be converted to APR.
PV = Present Value = £7,267 (your loan advance amount)
R = Repayments = £436.02 per quarter
r = quarterly interest rate (multiply by 4 to give annual equivalent and then convert to APR from quarterly compounding)
n = number of quarters = 20
To solve for r, you will need to do a little guess work and substitution. That's the beauty of calculators.
Hope this gives some comfort.
It is possible to calculate the APR using long-hand maths, but all those in the industry use calculators for the task.
If you have a financial calculator or even access to Excel, you can do the sums a lot easier.
Rate per thousand is used to enable a quote where the purchase price is not yet known or may vary. But it assumes a few constants. In your case:
Constant repayments are over 20 quarters, payable in arrears. No residual.
The APR of 7.4% is correct (using these assumptions).
The formula for calculating the interest rate is:
PV = R((1+r)n - 1)/r(1+r)n
Where you see "n" above, please read as 'power n' (as I can't denote a power symbol in this text) i.e. (1+r)to the power of n.
This formula will still only give you a quarterly compound interest rate, which would then need to be converted to APR.
PV = Present Value = £7,267 (your loan advance amount)
R = Repayments = £436.02 per quarter
r = quarterly interest rate (multiply by 4 to give annual equivalent and then convert to APR from quarterly compounding)
n = number of quarters = 20
To solve for r, you will need to do a little guess work and substitution. That's the beauty of calculators.
Hope this gives some comfort.
AB said:
Where does the £60/£1000 rate come from, it somehow knows it's being paid over 5 years.
They seem to have told you that over 5 yrs it will cost £60 per quarter for every £1000 borrowed.So £1000 for 5yrs would cost you £1200.
As you worked out, 7.267 times £1200 = £8720.40
Using one of the online calculators and putting numbers in until the answer looks about tight, the APR is approx. 7.5% (and 4% flat). Not sure why you'd want to know the maths behind how it's worked out? On straight loans, APR is close to 2x the flat rate.
The above assumes that it's just a normal loan, and there's nothing significant in your description of it as "lease purchase" which normally has a balloon (variable final payment) at the end.
AlasdairMc said:
Isn't it a requirement when selling loans and other financial products for the APR to be displayed more prominently than any other rate? Go back to vendor as said already.
Only for regulated finance agreements. Based on the fact that the vendor is quoting for quarterly repayments I'd assume it's unregulated as I don't know of any regulated customers who do pay quarterly!Sheepshanks said:
The above assumes that it's just a normal loan, and there's nothing significant in your description of it as "lease purchase" which normally has a balloon (variable final payment) at the end.
Lease Purchase, £0 residual at the end and kit purchased for option fee of £1 at the end of the term.Product is on the Energy Saving Technology List so ECA can be claimed on the payments this way. This is AIUI.
Reason I wanted to be able to calculate the interest rate myself is because it frustrates me that I don't know how to do it and I want to be able to do it!
Jarcy said:
Sheepshanks said:
4% flat
? - What's the flat rate? Is this assume no repayments are made? If that's the case, you're comparing apples & oranges.If you're comparing, then you ought to use APR.
Sheepshanks said:
There's no comparisons going on in this thread. Using the figures the OP gave, the flat rate is exactly 4%.
If you're comparing, then you ought to use APR.
Comparing Flat Rate to APR is apples and oranges, in any loan repayment situation.If you're comparing, then you ought to use APR.
The flat rate of (exactly) 4% is a totally irrelevant figure and only a round sum by virtue of the fact that the rate per thousand is a nice round £60.
e.g. plug in £65 and you get 6%, £70 = 8%, £80 = 12% and so forth. It's not a useful representation of the interest rate charge at all.
Any useful interest rate calculation must take into account the fact that the loan principal falls quarter-on-quarter. i.e. considering the time-value of money.
As you say, to compare different loan quotes you should use APR (AKA AER).
Jarcy said:
Comparing Flat Rate to APR is apples and oranges, in any loan repayment situation.
Dear God - Again, I'm not comparing anything. Simply stating that the flat rate is 4%.Jarcy said:
The flat rate of (exactly) 4% is a totally irrelevant figure and only a round sum by virtue of the fact that the rate per thousand is a nice round £60.
e.g. plug in £65 and you get 6%, £70 = 8%, £80 = 12% and so forth. It's not a useful representation of the interest rate charge at all.
No. It’s a nice round sum as the lender started off with 4%. They can’t start with APR as APR is a figure which can only be calculated once all the elements of the deal are known.e.g. plug in £65 and you get 6%, £70 = 8%, £80 = 12% and so forth. It's not a useful representation of the interest rate charge at all.
Jarcy said:
As you say, to compare different loan quotes you should use APR (AKA AER).
APR and AER are not the same. AER doesn’t include charges. Indeed while you can be certain the flat rate is exactly 4% you can’t be certain what the APR is. The OP may not have detailed all the charges, which are vital to knowing the APR. Sheepshanks said:
No. It’s a nice round sum as the lender started off with 4%. They can’t start with APR as APR is a figure which can only be calculated once all the elements of the deal are known.
Totally untrue on both points.No lender, (except perhaps loan sharks who charge crazy high interest) would ever start with a flat rate. They would be out of business extremely quickly without proper reference to their cost of capital, margin return, etc. Flat rate is a nonsense calculation in the finance world.
With any loan there are various parameters. You need to know some to calculate the rest. The interest rate is one such parameter, and that can be expressed as APR as a starting point.
Give me, 1 APR 2 Principal 3 Frequency 4 Duration 5 Residual 6 Due Advance/Arrears, and I will give you 7 Regular Instalment Amount and 8 Rate per Thousand. (assuming no fees)
Sheepshanks said:
APR and AER are not the same. AER doesn’t include charges. Indeed while you can be certain the flat rate is exactly 4% you can’t be certain what the APR is. The OP may not have detailed all the charges, which are vital to knowing the APR.
You are correct in that APR also includes charges. However we have already calculated the APR based on the parameters given and agree with the Ops stated APR, so can safely confirm no further fees are incorporated into this loan quote.The flat rate is not something expressed by finance lenders on their finance documents - but it used all the time all the time between finance companies and their intermediaries. It's the quickest way of calculating repayments on a hire purchase agreement.
For example - borrowing £10,000 at 4% flat rate (that is, 4% interest on original lend per year) over a 4 year term.
£10,000 x 4% = £400
£400 x 4 (years) = £1,600
£10,000 + £1,600 (capital plus interest) = £11,600
/48 (months) is £241.67.
The APR (which you can calculate using the formula above) takes into account that although you are paying capital back during your agreement, the interest charged is still fixed based on the original amount borrowed. (so for example in the figures above, after you'd paid 12 monthly payments there may be £8,500 worth of capital still to repay, but the interest is still calculated on the original £10,000 loan.) It also takes into account any document fees payable under the agreement.
As stated, when comparing loans, the APR is the rate you should be looking at as incorporates ALL charges.
For example - borrowing £10,000 at 4% flat rate (that is, 4% interest on original lend per year) over a 4 year term.
£10,000 x 4% = £400
£400 x 4 (years) = £1,600
£10,000 + £1,600 (capital plus interest) = £11,600
/48 (months) is £241.67.
The APR (which you can calculate using the formula above) takes into account that although you are paying capital back during your agreement, the interest charged is still fixed based on the original amount borrowed. (so for example in the figures above, after you'd paid 12 monthly payments there may be £8,500 worth of capital still to repay, but the interest is still calculated on the original £10,000 loan.) It also takes into account any document fees payable under the agreement.
As stated, when comparing loans, the APR is the rate you should be looking at as incorporates ALL charges.
rfoster said:
For example - borrowing £10,000 at 4% flat rate (that is, 4% interest on original lend per year) over a 4 year term.
£10,000 x 4% = £400
£400 x 4 (years) = £1,600
£10,000 + £1,600 (capital plus interest) = £11,600
/48 (months) is £241.67.
Suppose I took out the loan above, but instead of paying £241.67/month, they allowed me to pay nothing at all but pay £11,600 in one lump sum right at the end. What would the flat rate be on that loan.£10,000 x 4% = £400
£400 x 4 (years) = £1,600
£10,000 + £1,600 (capital plus interest) = £11,600
/48 (months) is £241.67.
Or supposing the loan made me pay back £11553 after 1 month, and then a pound a month for the remaining 47 months. What would the flat rate be then?
And if the answer to all scenarios is 4%, then it seems a complete waste of time even talking about it, as it tells you nothing about the value of the loan.
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